This paper presents a nano circuit of a full one-bit adder on the proposed five-input majority element. This innovative full adder design is used to development of a four-bit adder based on it. We offer a new single-bit full adder and a four-bit adder nano circuit in quantum-dot cellular automata technology. The proposed design four-bit adder utilizes only 231 quantum cells in a 0.49 µm2 area. It has a reduction in the number of cells, delay and energy dissipation at 1 K compared to the existing works. The QCADdesigner version 2.0.3 tool implements the developed quantum-dot cellular automata full adder and four-bit adder circuits. The implementation results show that the developed quantum-dot cellular automata full adder and four-bit adder circuits have an improvement over other quantum-dot cellular automata full adder circuits.